grad-pls-sem
用 PLS-SEM 處理小樣本和形成性構念，最大化內生構念的解釋變異
中文翻譯
--- name: "grad-pls-sem" description: "用偏最小平方結構方程模型（PLS-SEM），搭配反映性與形成性測量模型，最大化內生構念的解釋變異。當使用者樣本小、有形成性指標或是探索性模型，需要評估 AVE/CR/HTMT，或問到「該用 PLS 還是 CB-SEM」「形成性構念怎麼處理」「路徑係數的顯著性怎麼看」時，就用這個 skill。" metadata: category: "WP-31 量化方法" tags: ["PLS-SEM", "partial-least-squares", "SmartPLS", "formative", "reflective", "AVE", "HTMT"] --- # PLS-SEM 偏最小平方法結構方程模型 ## Overview PLS-SEM（Wold，1982；Hair 等人，2017）是以變異為基礎的結構方程模型取徑，估計以組合（composite）為基礎的路徑模型。和 CB-SEM 不同，它最大化內生構念的解釋變異，並且能輕易處理反映性和形成性兩種測量模型。 ## When to Use - 研究設計中有形成性測量模型 - 樣本數小（PLS 在 N ≥ 指向任一構念的最大路徑數的 10 倍時可行） - 研究目標是預測和解釋變異，不是驗證理論 - 結構模型複雜，有很多構念和指標 ## When NOT to Use - 研究目標是嚴格的理論檢驗和模型適配度評估 - 所有構念都是反映性的，而且樣本數足夠做 CB-SEM - 需要整體模型適配度指標（卡方、CFI、RMSEA） - 假設有循環關係（非遞迴模型） ## Assumptions ``` IRON LAW: PLS-SEM maximizes VARIANCE EXPLAINED, not model fit — it does NOT test overall model fit like CB-SEM. A high R² does not mean the model structure is correct. ``` 關鍵假設： 1. 預測變數的設定：每個構念都必須正確設定為反映性或形成性 2. 結構模型中沒有循環（非遞迴）關係 3. 觀察值彼此獨立（沒有擴充方法的話，不能有巢狀結構） 4. 資料不需要是常態分布（PLS 不假設分配） ## Methodology ### Step 1 — Specify Measurement Models 把每個構念分類為反映性（箭頭從構念指向指標）或形成性（箭頭從指標指向構念）。形成性構念至少需要兩個指標，並有理論依據。 ### Step 2 — Assess Reflective Measurement 評估指標信度（載荷 ≥ 0.70）、內部一致性（CR ≥ 0.70）、收斂效度（AVE ≥ 0.50），以及區辨效度（HTMT < 0.90）。 ### Step 3 — Assess Formative Measurement 透過 bootstrapping 檢查指標權重是否顯著。檢查指標之間的 VIF（VIF < 5.0）。評估內容效度，因為拿掉一個形成性指標，會改變構念的意義。 ### Step 4 — Evaluate Structural Model 報告路徑係數、R²、f² 效果量、Q² 預測相關性（透過 blindfolding），以及 bootstrap 信賴區間。演算法細節見 `references/`。 ## Output Format ```markdown ## PLS-SEM Analysis: [Study Title] ### Reflective Measurement Assessment | Construct | Indicator | Loading | CR | AVE | HTMT | |-----------|-----------|---------|-----|-----|------| | [name] | [item] | x.xx | x.xx | x.xx | x.xx | ### Formative Measurement Assessment | Construct | Indicator | Weight | VIF | p-value | |-----------|-----------|--------|-----|---------| | [name] | [item] | x.xx | x.xx | x.xx | ### Structural Model | Path | β | t-value | p-value | f² | Supported? | |------|---|---------|---------|-----|------------| | X → Y | x.xx | x.xx | x.xx | x.xx | [Yes/No] | ### Model Quality | Endogenous Construct | R² | Q² | |---------------------|-----|-----| | [name] | x.xx | x.xx | ### Limitations - [Note any assumption violations] ``` ## Gotchas - PLS-SEM 不是小樣本的萬靈丹，它仍然需要足夠的統計檢定力 - 把反映性誤設為形成性（或反過來），會從根本上改變結果 - 在 PLS-SEM 中，區辨效度偏好用 HTMT，不用 Fornell-Larcker - PLS 會高估載荷、低估路徑係數（大樣本一致性 PLSc 可以修正） - Blindfolding 的 Q² > 0 顯示有預測相關性，但不能驗證模型結構 - 用 CB-SEM 的標準（CFI、RMSEA）報告 PLS 的結果，在方法上是錯的 ## References - Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). *A Primer on Partial Least Squares Structural Equation Modeling* (2nd ed.). Sage. - Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity. *Journal of the Academy of Marketing Science*, 43(1), 115-135. - Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report PLS-SEM. *European Business Review*, 31(1), 2-24.
英文原文
--- name: "grad-pls-sem" description: "Apply Partial Least Squares SEM (PLS-SEM) with reflective and formative measurement models to maximize explained variance in endogenous constructs. Use this skill when the user has small samples, formative indicators, or exploratory models, needs to assess AVE/CR/HTMT, or when they ask 'should I use PLS or CB-SEM', 'how do I handle formative constructs', or 'what is the path coefficient significance'." metadata: category: "WP-31 量化方法" tags: ["PLS-SEM", "partial-least-squares", "SmartPLS", "formative", "reflective", "AVE", "HTMT"] --- # PLS-SEM 偏最小平方法結構方程模型 ## Overview PLS-SEM (Wold, 1982; Hair et al., 2017) is a variance-based approach to structural equation modeling that estimates composite-based path models. Unlike CB-SEM, it maximizes explained variance in endogenous constructs and readily handles both reflective and formative measurement models. ## When to Use - Formative measurement models are part of the research design - Sample size is small (PLS works with N ≥ 10× the largest number of paths pointing to any construct) - Research goal is prediction and variance explanation rather than theory confirmation - The structural model is complex with many constructs and indicators ## When NOT to Use - Research goal is strict theory testing and model fit assessment - All constructs are reflective and sample size is adequate for CB-SEM - You need global model fit indices (chi-square, CFI, RMSEA) - Circular relationships (non-recursive models) are hypothesized ## Assumptions ``` IRON LAW: PLS-SEM maximizes VARIANCE EXPLAINED, not model fit — it does NOT test overall model fit like CB-SEM. A high R² does not mean the model structure is correct. ``` Key assumptions: 1. Predictor specification — each construct must be correctly specified as reflective or formative 2. No circular (non-recursive) relationships in the structural model 3. Observations are independent (no nested structure without extensions) 4. Data need not be normally distributed (PLS is distribution-free) ## Methodology ### Step 1 — Specify Measurement Models Classify each construct as reflective (arrows from construct to indicators) or formative (arrows from indicators to construct). Formative constructs require at minimum two indicators and a theoretical rationale. ### Step 2 — Assess Reflective Measurement Evaluate indicator reliability (loadings ≥ 0.70), internal consistency (CR ≥ 0.70), convergent validity (AVE ≥ 0.50), and discriminant validity (HTMT < 0.90). ### Step 3 — Assess Formative Measurement Check indicator weights for significance via bootstrapping. Examine VIF among indicators (VIF < 5.0). Assess content validity — dropping a formative indicator changes the construct meaning. ### Step 4 — Evaluate Structural Model Report path coefficients, R², f² effect sizes, Q² predictive relevance (via blindfolding), and bootstrapped confidence intervals. See `references/` for algorithm details. ## Output Format ```markdown ## PLS-SEM Analysis: [Study Title] ### Reflective Measurement Assessment | Construct | Indicator | Loading | CR | AVE | HTMT | |-----------|-----------|---------|-----|-----|------| | [name] | [item] | x.xx | x.xx | x.xx | x.xx | ### Formative Measurement Assessment | Construct | Indicator | Weight | VIF | p-value | |-----------|-----------|--------|-----|---------| | [name] | [item] | x.xx | x.xx | x.xx | ### Structural Model | Path | β | t-value | p-value | f² | Supported? | |------|---|---------|---------|-----|------------| | X → Y | x.xx | x.xx | x.xx | x.xx | [Yes/No] | ### Model Quality | Endogenous Construct | R² | Q² | |---------------------|-----|-----| | [name] | x.xx | x.xx | ### Limitations - [Note any assumption violations] ``` ## Gotchas - PLS-SEM is NOT a silver bullet for small samples — it still requires adequate statistical power - Misspecifying reflective as formative (or vice versa) fundamentally changes results - HTMT is preferred over Fornell-Larcker for discriminant validity in PLS-SEM - PLS overestimates loadings and underestimates path coefficients (consistency at large corrects this) - Blindfolding Q² > 0 shows predictive relevance but does not validate the model structure - Reporting PLS results using CB-SEM criteria (CFI, RMSEA) is methodologically incorrect ## References - Hair, J. F., Hult, G. T. M., Ringle, C. M., & Sarstedt, M. (2017). *A Primer on Partial Least Squares Structural Equation Modeling* (2nd ed.). Sage. - Henseler, J., Ringle, C. M., & Sarstedt, M. (2015). A new criterion for assessing discriminant validity. *Journal of the Academy of Marketing Science*, 43(1), 115-135. - Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report PLS-SEM. *European Business Review*, 31(1), 2-24.